Not including the reservations that require a credit card hold, I have never had a problem. If something does come up at the last minute, I do try to call the Disney dining number from my cell phone and let them know I will not be able to make the reservation...that way a standby family may get in much sooner. That being said, I have never had to cancel or no show more than 1 or MAYBE 2 reservations on a trip...I'm not sure if Dsiney has a procedure in place if you don't show up for a 3rd or 4th ressie. Like you, we also travel with two little ones and things always seem to come up...this trip DS6 and DS2. We take advantage of TS meals as a time to slow down the pace, cool off, talk about the fun things we have done so far, plan what we want to do next, and relax over a nice meal.
I wouldn't worry about it too much. Enjoy your trip!